I am a Ph.D student with F-1 visa,
which is a non-immigrant visa. Do I have to wait to apply for the Green Card in
EB1-Extraordinary Ability after my graduation and changing the visa to H-1B?

Answer:

The F-1 visa is a
non-immigrant visa, but it does not mean that a F-1 visa holder is not allowed
to apply for the Green Card. A non-immigrant visa holder, such as F-1 and J-1,
may change its intent thereafter receiving a nonimmigrant visa.

It is not true that a
non-immigrant visa holder must change its visa type to a nonimmigrant visa such
as H or L visa, which allows dual intent, before aGreen Card petition can be filed. Generally speaking, anyone can file an
immigration petition at any time if he/she meets the qualification requirements.
But, if your current F-1 visa
is not long enough for you to finish your degree, it is better to wait the Green
Card application until you have extended your F-1 visa.